{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:3ALDDILSPJDE5FV7NF2OEP6PBN","short_pith_number":"pith:3ALDDILS","schema_version":"1.0","canonical_sha256":"d81631a1727a464e96bf6974e23fcf0b47dcc3664416a17bd907a960033c94fd","source":{"kind":"arxiv","id":"1907.10527","version":1},"attestation_state":"computed","paper":{"title":"Affine commutative-by-finite Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Kenneth Brown, Miguel Couto","submitted_at":"2019-07-24T15:40:16Z","abstract_excerpt":"The objects of study in this paper are Hopf algebras $H$ which are finitely generated algebras over an algebraically closed field and are extensions of a commutative Hopf algebra by a finite dimensional Hopf algebra. Basic structural and homological properties are recalled and classes of examples are listed. Bounds are obtained on the dimensions of simple $H$-modules, and the structure of $H$ is shown to be severely constrained when the finite dimensional extension is semisimple and cosemisimple."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1907.10527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-07-24T15:40:16Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"2ec91d40f12a7d37b2d08154f053c4e95d551454d8e4d5a796016b3e1388729a","abstract_canon_sha256":"2c46e49166208089a3445f35df9f64007a28d34b814a8173d200f84b10b58a33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:37.649280Z","signature_b64":"KMmIvJghUmW4VSKwzU5Cmwe+FuCATPAkkFi5su+SiYOpDu97XYsvOc43PbMFn8HGgIvGUTY6w2TibSyWF4AIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d81631a1727a464e96bf6974e23fcf0b47dcc3664416a17bd907a960033c94fd","last_reissued_at":"2026-05-17T23:39:37.648631Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:37.648631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine commutative-by-finite Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Kenneth Brown, Miguel Couto","submitted_at":"2019-07-24T15:40:16Z","abstract_excerpt":"The objects of study in this paper are Hopf algebras $H$ which are finitely generated algebras over an algebraically closed field and are extensions of a commutative Hopf algebra by a finite dimensional Hopf algebra. Basic structural and homological properties are recalled and classes of examples are listed. Bounds are obtained on the dimensions of simple $H$-modules, and the structure of $H$ is shown to be severely constrained when the finite dimensional extension is semisimple and cosemisimple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10527","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.10527","created_at":"2026-05-17T23:39:37.648733+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.10527v1","created_at":"2026-05-17T23:39:37.648733+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10527","created_at":"2026-05-17T23:39:37.648733+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ALDDILSPJDE","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ALDDILSPJDE5FV7","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ALDDILS","created_at":"2026-05-18T12:33:07.085635+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3ALDDILSPJDE5FV7NF2OEP6PBN","json":"https://pith.science/pith/3ALDDILSPJDE5FV7NF2OEP6PBN.json","graph_json":"https://pith.science/api/pith-number/3ALDDILSPJDE5FV7NF2OEP6PBN/graph.json","events_json":"https://pith.science/api/pith-number/3ALDDILSPJDE5FV7NF2OEP6PBN/events.json","paper":"https://pith.science/paper/3ALDDILS"},"agent_actions":{"view_html":"https://pith.science/pith/3ALDDILSPJDE5FV7NF2OEP6PBN","download_json":"https://pith.science/pith/3ALDDILSPJDE5FV7NF2OEP6PBN.json","view_paper":"https://pith.science/paper/3ALDDILS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.10527&json=true","fetch_graph":"https://pith.science/api/pith-number/3ALDDILSPJDE5FV7NF2OEP6PBN/graph.json","fetch_events":"https://pith.science/api/pith-number/3ALDDILSPJDE5FV7NF2OEP6PBN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ALDDILSPJDE5FV7NF2OEP6PBN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ALDDILSPJDE5FV7NF2OEP6PBN/action/storage_attestation","attest_author":"https://pith.science/pith/3ALDDILSPJDE5FV7NF2OEP6PBN/action/author_attestation","sign_citation":"https://pith.science/pith/3ALDDILSPJDE5FV7NF2OEP6PBN/action/citation_signature","submit_replication":"https://pith.science/pith/3ALDDILSPJDE5FV7NF2OEP6PBN/action/replication_record"}},"created_at":"2026-05-17T23:39:37.648733+00:00","updated_at":"2026-05-17T23:39:37.648733+00:00"}